Hello Akalifans.
Akali is very easy to play in lane 'cause of her Q, just cast it regualary, later you get your E too and that will do most of the work.
You try to last hit with that and if you get ganked or have problmes with your opponent just put your W (be sure to have enough energy for that) and you are rescued (if not you still have flash)

Akali is best played in midlane because she doesn't get countered to easy in this lane, if you want to play here top beware of the tanky/damage dealing champs like Darius or Garen.
In midlane you should be ware off Swain and Mordekaiser and if she is good played also Diana.

What you need to do is be very patient 'till level 6, then you can start rocking your opponent.
Wait until your 3 uiltimates are ready and try to poke while doing an immensive ammount of damage.
If the opponent is pushing hard attack him right away, but beware off minions at the beginning.
When you're close to your opponent with your ultimate cast your circle so that he is slowed and can't see you.
While fighting do not forget your ignite, use when you think you can beat your opponent right after your first or second ultimate, so he can't flash or jump out of range, and you get your 5 extra AP while waiting for Ignite to be ready again.
But don't be to focused on your lane! Akali is a good ganker and if the situation allows it, you should help yor mates bot and top.

We assume that you already rocked your earlygame with Akali and even if you didn't still nothing is lost.
Akali starts to work really well with her itmes, espacially against the opponents carrys when they are not feeded to hard.
Don't be afraid of 1on1 with opponents, you can easily kill the most of them, but if it takes you too long, think of teammates who could come to rescue.
In teamfights you should wait for the tank to engage and than jump in. Try to focus the carry and get assists or kills so that you can use your ultimate more often. Cast your circle right after you jumped in with your ultimate, so that you can't be focused so easily.

So with this build you are an offtank-like Akali which can't be killed to easy but still deals a heck of damage.
Be patient 'till level 6 and start to rock with your ultimate.